Stochastic Intensity Models of Wrong Way Risk:Wrong Way CVA Need Not Exceed Independent CVA

Abstract

A financial institution's counterparty credit exposures may be correlated with the credit quality of a counterparty; wrong way risk refers to the case where this correlation is negative. Hull and White [9] are the first to model wrong way risk in Credit Value Adjustment (CVA) calculations by expressing the counterparty's default intensity in terms of the financial institution's credit exposure to the counterparty. We derive a formula for CVA for a class of models that includes the formulation of Hull and White [9], and we show that wrong way risk does not affect the credit quality of the counterparty. We provide numerical examples based on the Hull and White [9] formulation to estimate CVA for forward contracts and European options. These examples demonstrate that independent CVA can exceed wrong way CVA. This is inconsistent with the scalar multiples of independent CVA that have been adopted by regulators as a proxy for wrong way CVA.